On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics

TL;DR

This paper explores shock wave phenomena in Bose-Einstein condensates, demonstrating that dispersive shock waves, rather than dissipative ones, explain experimental observations through theoretical, numerical, and experimental comparisons.

Contribution

It introduces a dispersive shock wave framework for BECs, contrasting it with classical dissipative shocks, supported by numerical simulations and experimental validation.

Findings

Dispersive shock waves accurately model BEC shock phenomena

Numerical simulations align well with experimental results

Dispersive shocks differ significantly from dissipative shocks in structure and speed

Abstract

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, eg. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with the three dimensional experiment show that three and two dimensional approximations are in excellent agreement and one dimensional approximations are in good qualitative agreement. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.